added Best First search in search.ipynb (#708)

* added Best First search

* fixed minor conflicts

* minor changes

Author: nvinayvarma189

search.ipynb

@@ -41,6 +41,7 @@
     "* Breadth-First Search\n",
     "* Uniform Cost Search\n",
     "* A\\* Search\n",
+    "* Best First Search\n",
     "* Genetic Algorithm"
    ]
   },
@@ -447,7 +448,7 @@
     "2. Depth First Tree Search - Implemented\n",
     "3. Depth First Graph Search - Implemented\n",
     "4. Breadth First Search - Implemented\n",
-    "5. Best First Graph Search\n",
+    "5. Best First Graph Search - Implemented\n",
     "6. Uniform Cost Search - Implemented\n",
     "7. Depth Limited Search\n",
     "8. Iterative Deepening Search\n",
@@ -1190,7 +1191,7 @@
    ],
    "source": [
     "all_node_colors = []\n",
-    "romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)\n",
+    "romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)\n", 
     "display_visual(user_input = False, algorithm = astar_search, problem = romania_problem)"
    ]
   },
@@ -1253,6 +1254,128 @@
     "display_visual(user_input = True)"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## BEST FIRST SEARCH\n",
+    "Let's change all the node_colors to starting position and define a different problem statement."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 23,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def best_first_graph_search(problem, f):\n",
+    "    \"\"\"Search the nodes with the lowest f scores first.\n",
+    "    You specify the function f(node) that you want to minimize; for example,\n",
+    "    if f is a heuristic estimate to the goal, then we have greedy best\n",
+    "    first search; if f is node.depth then we have breadth-first search.\n",
+    "    There is a subtlety: the line \"f = memoize(f, 'f')\" means that the f\n",
+    "    values will be cached on the nodes as they are computed. So after doing\n",
+    "    a best first search you can examine the f values of the path returned.\"\"\"\n",
+    "    \n",
+    "    # we use these two variables at the time of visualisations\n",
+    "    iterations = 0\n",
+    "    all_node_colors = []\n",
+    "    node_colors = dict(initial_node_colors)\n",
+    "    \n",
+    "    f = memoize(f, 'f')\n",
+    "    node = Node(problem.initial)\n",
+    "    \n",
+    "    node_colors[node.state] = \"red\"\n",
+    "    iterations += 1\n",
+    "    all_node_colors.append(dict(node_colors))\n",
+    "    \n",
+    "    if problem.goal_test(node.state):\n",
+    "        node_colors[node.state] = \"green\"\n",
+    "        iterations += 1\n",
+    "        all_node_colors.append(dict(node_colors))\n",
+    "        return(iterations, all_node_colors, node)\n",
+    "    \n",
+    "    frontier = PriorityQueue(min, f)\n",
+    "    frontier.append(node)\n",
+    "    \n",
+    "    node_colors[node.state] = \"orange\"\n",
+    "    iterations += 1\n",
+    "    all_node_colors.append(dict(node_colors))\n",
+    "    \n",
+    "    explored = set()\n",
+    "    while frontier:\n",
+    "        node = frontier.pop()\n",
+    "        \n",
+    "        node_colors[node.state] = \"red\"\n",
+    "        iterations += 1\n",
+    "        all_node_colors.append(dict(node_colors))\n",
+    "        \n",
+    "        if problem.goal_test(node.state):\n",
+    "            node_colors[node.state] = \"green\"\n",
+    "            iterations += 1\n",
+    "            all_node_colors.append(dict(node_colors))\n",
+    "            return(iterations, all_node_colors, node)\n",
+    "        \n",
+    "        explored.add(node.state)\n",
+    "        for child in node.expand(problem):\n",
+    "            if child.state not in explored and child not in frontier:\n",
+    "                frontier.append(child)\n",
+    "                node_colors[child.state] = \"orange\"\n",
+    "                iterations += 1\n",
+    "                all_node_colors.append(dict(node_colors))\n",
+    "            elif child in frontier:\n",
+    "                incumbent = frontier[child]\n",
+    "                if f(child) < f(incumbent):\n",
+    "                    del frontier[incumbent]\n",
+    "                    frontier.append(child)\n",
+    "                    node_colors[child.state] = \"orange\"\n",
+    "                    iterations += 1\n",
+    "                    all_node_colors.append(dict(node_colors))\n",
+    "\n",
+    "        node_colors[node.state] = \"gray\"\n",
+    "        iterations += 1\n",
+    "        all_node_colors.append(dict(node_colors))\n",
+    "    return None\n",
+    "\n",
+    "def best_first_search(problem, h=None):\n",
+    "    \"\"\"Best-first graph search is an informative searching algorithm with f(n) = h(n).\n",
+    "    You need to specify the h function when you call best_first_search, or\n",
+    "    else in your Problem subclass.\"\"\"\n",
+    "    h = memoize(h or problem.h, 'h')\n",
+    "    iterations, all_node_colors, node = best_first_graph_search(problem, lambda n: h(n))\n",
+    "    return(iterations, all_node_colors, node)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 39,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "5ae2d521b74743afa988c462a851c269"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "application/vnd.jupyter.widget-view+json": {
+       "model_id": "559c20b044a4469db7f0ab8c3fae1022"
+      }
+     },
+     "metadata": {},
+     "output_type": "display_data"
+    }
+   ],
+   "source": [
+    "all_node_colors = []\n",
+    "romania_problem = GraphProblem('Arad', 'Bucharest', romania_map)\n",
+    "display_visual(user_input = False, algorithm = best_first_search, problem = romania_problem)"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},